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I/MR/S Chart with Unequal Sample Size

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  • #246294

    PharmaUser1
    Participant

    Hello community,

    i have a rather specific problem and am keen to hear your solutions. It´s about the choice of an appropriate control chart and limits.

    My situation:

    • Batch production with higher inter-batch than intra-batch variation due to variation in basic materials which cannot be eliminated – > My conclusion X-Bar / s chart (intra standard deviation determining control limits) is too strict, many false alarms (evidence by Wheeler / Chambers, Understanding Statistical Process Control)
    • I / MR with I calculated as an average value per batch doesn´t cover the intra-batch variation

    My thought:

    • Choosing an threeway I / MR / s – Chart, where I is calculated as an average value per batch and the control limits are derived by the common way via MR plus a s-chart where control limits are derived via s itself and which covers the intra-batch variation (this idea is also suggested by Wheeler / Chambers, Understanding Statistical Process Control)

    My problem:

    • The limits for the I-Chart are derived without taking into account the sample size per batch from which the batch average (I in the chart) was derived. However if there are big differences e. g, some batches consisting of 100 values cause they take longer to manufacture and some of 20, there are different effects of smoothing my average and the control limits for the bigger batch should be tighter for this reason.

    Does anybody have plans to solve this dilemma?

    Here there is an example attached of the threeway chart. However Minitab only computes these if sample sizes are equal.

    • This topic was modified 1 month, 1 week ago by PharmaUser1.
    • This topic was modified 1 month, 1 week ago by Katie Barry.
    • This topic was modified 1 month, 1 week ago by Katie Barry.
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    #246444

    Jay Arthur
    Participant

    Have you considered using both XbarS and IMRR?

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    #246698

    Todd Hatley
    Participant

    I agree with Jay. The IMR chart is for plotting individual data points. If your data is saved sequentially, you could plot every data point instead of samples. If you are interested in evaluating the average performance of the process consider using the XbarR or XbarS chart.

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